how many eggs

[turnergraphics]

how many dozen eggs would you have on the last day if you doubled an egg everyday for thirty days? (my key question is, do you have 1 egg on day 1, or do you double that one egg to make 2)...or ....????

 

[Denis]

1 + 2 + 4 + 8 .....

 

[mmm4444bot]

if you doubled an egg everyday

Do you understand the meaning of the indefinite article "an" ?

The phrase "an egg" refers to a single egg.

Therefore, only one egg doubles each day.

As to your confusion about "everyday", you can think of the doubling taking place at the end of the day.

On day 1, you start with one egg. At the end of day 1, it doubles. Now there are two.

On day 2, you start with two eggs; one of them doubles. At the end of day 2, there are three.

On day 3, you start with three eggs; one of them doubles. At the end of day 3, there are four.

On day 4, you start with four eggs and you end with five, et cetera.

In other words, at the end of each day, there is one more egg than the day number.

So, there will be thirty-one eggs at the end of the 30th day.

That's 31/12 dozen eggs.

Seems like a dumb exercise, to me.

But, maybe your teacher is scrambled.

(Of course, Denis has egg on the face because Denis has over 89 million cartons of eggs to eat. Very messy.)

 

[soroban]

Hello, turnergraphics!

If that's the original wording of the problem . . . sloppy!

How many dozen eggs would you have on the last day
if you doubled an egg everyday for thirty days?

\(\displaystyle \begin{array}{c}\text{I assume we start with 1 egg on the 1st day.}\\ \text{We have 2 eggs on the 2nd day.} \\ \text{We have 4 eggs on the 3rd day.}\\ \text{We have 8 eggs on the 4th day.} \\ \vdots \\ \text{We have }x\text{ eggs on the 30th day.} \end{array}\)


\(\displaystyle 1, 2, 4, 8, \hdots\,\text{ is a geometric }sequence\)
. . \(\displaystyle \text{with first term }a = 1\,\text{ and common ratio }r = 2.\)

. . \(\displaystyle \text{The }n^{th}\text{ term is: }\:a_n \:=\:2^{n-1}\)


\(\displaystyle \text{On the }30^{th}\text{ day, we have: }\:2^{29} \:=\:536,\!870,\!912\text{ eggs} \;=\;44,\!739,\!242\tfrac{2}{3}\text{ dozen eggs.}\)

 

[Denis]

\(\displaystyle \text{On the }30^{th}\text{ day, we have: }\:2^{29} \:=\:536,\!870,\!912\text{ eggs} \;=\;44,\!739,\!242\tfrac{2}{3}\text{ dozen eggs.}\)

But not enough to handle the demand for Egg McMuffins :roll:

 

[mmm4444bot]

Oops, I see that I forgot to subtract 1 from n, in my rushed giddiness to make fun of Denis.

(sigh)

Denis, Loren and I are serving breakfast, in the corner.

 

[Denis]

Re:

Oops, I see that I forgot to subtract 1 from n, in my rushed giddiness to make fun of Denis.

But you'd be ok in January, March, May, July, August, October and December :idea: